Microwave heating of materials with impurities

Abstract

The microwave heating of materials is important in many industrial processes. For example, it is used for the smelting of metals and the sintering of ceramics. Hot-spots (localised areas of high temperature) can develop in the material being heated or in the microwave oven itself, with disastrous consequences. Impurities in the material or in a component of the microwave oven can have different electromagnetic and thermal properties to the surrounding material. Different rates of heating occur at these sites, which gives rise to differential heating, which can lead to the generation of hot-spots. The generation of hot-spots by this mechanism is considered for a finite one-dimensional slab with a single impurity at its centre. A fixed-temperature boundary condition is applied at both ends of the slab and one end of the slab is irradiated by microwaves of constant amplitude. The heat absorption at the impurity is assumed to have a power-law dependence on temperature (hence hot-spot generation can occur via thermal runaway). Depending on the electrical and thermal properties of the material there are two possibilities; either a hot-spot occurs or a steady-state solution occurs due to a balance between heat absorption in the material and heat loss through the boundaries. These steady-state solutions are found for both linear and non-linear thermal absorptivity and constant and decaying electric-field amplitude. If possible the region of parameter space in which they occur (in the rest of the parameter space hot-spots occur) is also found. In addition, numerical solutions are developed to verify the steady-state solutions and to investigate cases where analytical solutions are difficult to derive, such as for materials with multiple impurities.